Problem: Express this quotient in scientific notation: ${\frac{1.100\times 10^{-3}} {2.0\times 10^{-2}}}$
Answer: Start by collecting like terms together. $= {\frac{1.100} {2.0}} \times{\frac{10^{-3}} {10^{-2}}}$ Then divide each term separately. When dividing exponents with the same base, subtract their powers. $= 0.55 \times 10^{-3\,-\,-2}$ $= 0.55 \times 10^{-1}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the right without changing the value of our answer. $ $ We can use the fact that $0.55$ is the same as $5.50 \div 10$ , or $5.50 \times 10^{-1}$ $ = {5.50 \times 10^{-1}} \times 10^{-1} $ $= 5.50\times 10^{-2}$